Table of Contents
What is linear elastic deformation?
A linear elastic material is a mathematical model used to analyze the deformation of solid bodies. It is useful to compute the relation between the forces applied on the object and the corresponding change in shape. In other terms, it relates the stresses and the strains in the material.
What is the formula of deformation?
Deformation of a body is expressed in the form x = F(X) where X is the reference position of material points of the body. Such a measure does not distinguish between rigid body motions (translations and rotations) and changes in shape (and size) of the body. A deformation has units of length.
What is an isotropic elastic material?
A material is said to be isotropic if its properties do not vary with direction. Isotropic materials therefore have identical elastic modulus, Poisson’s ratio, coefficient of thermal expansion, thermal conductivity, etc. in all directions.
What is the linear elastic region?
Linear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics.
What is the formula for elastic force?
2.1. 1 Basic Spring Elements and Stiffness
| Translation | Rotation | |
|---|---|---|
| Elastic force/moment | f e = k t · Δ x = k t · ( x 1 − x 2 ) | m e = k r · Δ θ = k r · ( θ 1 − θ 2 ) |
| Elastic potential energy | U e = 1 2 · k t · ( Δ x ) 2 = 1 2 · k t · ( x 1 − x 2 ) 2 | U e = 1 2 · k r · ( Δ θ ) 2 = 1 2 · k r · ( θ 1 − θ 2 ) 2 |
What is the formula for elastic force Mcq?
Solution: The law states that the strain in a solid is proportional to the applied stress within the elastic limit of that solid body i.e. stress = k x strain.
What is linear isotropic elastic?
A material is said to be isotropic if its properties do not vary with direction. Isotropic materials therefore have identical elastic modulus, Poisson’s ratio, coefficient of thermal expansion, thermal conductivity, etc.
How do you calculate deformation rate?
HOOKE’S LAW F=kΔL, whereΔL is the amount of deformation (the change in length, for example) produced by the forceF, andk is a proportionality constant that depends on the shape and composition of the object and the direction of the force. Figure 1. A graph of deformation ΔL versus applied force F.
Is steel linear elastic?
This means that steel is a nice material to model with linear elasticity, as long as you don’t reach strains (and stresses) that would cause yielding.
Does elastic deformation really exist?
Elastic deformation and elastic strain is a transitory dimensional change that exists only while the initiating stress is applied and disappears immediately upon removal of the stress. When a metal is subjected to a load (force), it is distorted or deformed, no matter how strong the metal or light the load.
What is the ratio of the elastic modulus?
The elastic modulus is a material property that describes its stiffness and is therefore one of the most important properties of solid materials. It is the ratio of stress to strain when deformation is totally elastic. Stress is defined as force per unit area and strain as elongation or contraction per unit length.
What are the four elastic constants for steel?
2.1. Density functional theory. The model was described by a 16-atom cubic supercell built from 2 × 2 × 1 fcc.
What is the formula of the elastic force?
What is the formula for elastic force? Elastic potential energy is equal to the force times the distance of movement. Elastic potential energy = force x distance of displacement. Because the force is = spring constant x displacement, then the Elastic potential energy = spring constant x displacement squared. Click to see full answer.